Monopole antenna

ABSTRACT

The present invention relates to a monopole antenna comprising: a radiator arranged in the center of a front surface of a dielectric substrate, and including a plurality of loops formed in a structure in which a Mobius strip is cut at least one time along the circumference; a first bridge for sequentially connecting one end of each loop; and a second bridge for connecting via-holes respectively formed at one end of the innermost loop and the outermost loop, thereby obtaining an effect of enabling an antenna, to which a quasi-Mobius strip and a via-hole structure are applied, to be miniaturized.

TECHNICAL FIELD

The present invention relates to a monopole antenna, and moreparticularly, to a monopole antenna applicable to a wirelesscommunication system.

BACKGROUND ART

As wireless mobile communications evolve rapidly, various wirelesscommunication systems such as 4G/5G mobile communication terminals,wireless control systems, Machine to Machine (M2M), and Internet ofThings (IoT) require elements which are more lightweight, have a simplestructure, and are miniaturized into a structure that facilitatesintegration.

Accordingly, various schemes for reducing a physical size of a circuithave been studied, and flat microwave elements and circuits have beenwidely developed and applied because they are easy to design andmanufacture.

In particular, manufacturers of mobile communication terminals andwireless control systems in the world require a miniaturized, flexible,broadband, high-gain antenna which is operated at a low power with highradiation efficiency and has no spatial constraints when mounted in acircuit.

As miniaturization schemes for such an antenna, various schemes such asa scheme of applying a helical structure and a scheme of applying ameta-material and a stacked structure are applied.

Among the above schemes, since a resonance frequency is generated perone rotation around a circumference, the helical structure is notsuitable for a scheme of miniaturizing an antenna having a singleresonance frequency characteristic. In addition, schemes of applying themeta-material and the stacked structure have a disadvantage in that aconfiguration is complicated and a manufacturing cost is increased.

In addition, the technology utilizing a basic Moebius strip having athree-dimensional structure and the technology of a flat structureutilizing a characteristic of a Moebius strip have been proposed.However, the above flat structure is not a perfect flat structure, and aline coupling effect occurs at a low frequency.

An example of such broadband monopole antenna technology according tothe related art is disclosed in Korean Patent Registration No.10-0416883 (issued on Feb. 5, 2004), Korean Patent Registration No.10-0660051 (issued on Dec. 22, 2006), etc.

DISCLOSURE Technical Problem

However, a compact antenna according to the related art has aconfiguration of a low-cost printed patch antenna including a metalground, a substrate with a high dielectric constant, and a radiator.

When such a printed patch antenna is applied to a reception module, aceramic material having a high dielectric constant lowers radiationefficiency of a reception antenna, and an electromagnetic interference(EMI) occurs, thereby degrading reception sensitivity of a receiver.

In addition, the compact antenna according to the related art is limitedin that an antenna installation space has to be ensured.

To solve the problems described above, an object of the presentinvention is to provide a miniaturized monopole antenna capable ofoperating at a low power by using an electrode pattern on a flexiblesubstrate, and improving the radiation efficiency.

In addition, another object of the present invention is to provide amonopole antenna in which the antenna is miniaturized by using aquasi-Moebius strip structure, and high-performance antennacharacteristics, which are wideband and high-gain characteristics, areimplemented.

Still another object of the present invention is to provide a monopoleantenna capable of controlling directivity of a radiation pattern of theantenna by adjusting a rotation angle of a ring.

Technical Solution

To achieve the objects described above, according to the presentinvention, there is provided a monopole antenna including: a radiatorarranged on a center of a front surface of a dielectric substrate, andincluding a plurality of loops formed in a structure in which aquasi-Moebius strip is cut at least one time along a circumference; afirst bridge for sequentially connecting one end of each of the loops;and a second bridge for connecting via-holes respectively formed at oneend of an innermost loop and an outermost loop.

Advantageous Effects

As described above, according to the monopole antenna of the presentinvention, an ultra-wideband antenna (UWB antenna) employing aquasi-Moebius strip and a via-hole structure can be miniaturized.

In other words, according to the present invention, a length of aphysical circumference is reduced by 1/(N+1) times as compared with aconventional ring antenna. While a resonance frequency is generated perone rotation around a circumference, the present invention can obtain anultra-wideband characteristic ranging from about 2 GHz to 10 GHz byemploying the quasi-Moebius strip and the via-hole.

In addition, according to the present invention, a radiation pattern ina far-field exhibits omni-directional characteristics similar to atypical monopole antenna, and directivity can be controlled by adjustinga rotation angle of each ring provided in a radiator.

Further, according to the present invention, the resonance frequency anda reflection coefficient are adjustable by varying three parameters ofthe quasi-Moebius strip, that is, a thickness of a ring line of thequasi-Moebius strip, a width of a bridge, and a radius and a position ofthe via-hole, and simulation results show that the quasi-Moebius striphaving the via-hole structure can be applied to a matching network.

In addition, according to the present invention, the thickness of thering line and a size and the position of the via-hole affect aninductance (L), and the width of the bridge and the size and position ofthe via-hole affect a capacitance (C), so that the three parameters ofthe quasi-Moebius strip can be applied to a matching circuit.

In other words, according to simulation and measurement results, theresonance frequency of a quasi-Moebius strip antenna is within a 2.4 GHzband, a peak value of a reflection coefficient S11 is 17.3 dB in thesimulation result, and 27.65 dB in the measurement result.

Therefore, according to the present invention, an optimizedquasi-Moebius strip is applied to the antenna so that the antenna isconfigured as a plurality of ring lines having mutually different radii,but the antenna can have a single resonance frequency characteristic.

In addition, according to the present invention, when a miniaturized UWBantenna is applied to a multiple-input multiple-output antenna (MIMOantenna), an envelope correlation coefficient value (ECC value)indicating correlation between antennas is 0.02 or less in a frequencyrange of 3 GHz to 8 GHz, so that spectrum efficiency can be improved.

Further, according to the present invention, the quasi-Moebius striphaving the via-hole structure can be applied to RF passive elements suchas an oscillator and a resonator as well as the UWB antenna, therebyminiaturizing the RF passive elements.

DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram showing a circular disc-shaped monopoleantenna having a coplanar waveguide transmission line implemented on adielectric substrate.

FIGS. 2A to 2C are conceptual diagrams showing surface currentdistribution for each operating frequency of the circular disc monopoleantenna at a feeding phase of 0°.

FIG. 3 is a block diagram showing a circular double-closed-loop monopoleantenna for miniaturizing a structure of the circular disc monopoleantenna.

FIGS. 4A and 4B are views showing input matching characteristics of thecircular double-closed-loop monopole antenna which is subject to asimulation for optimization.

FIG. 5 is a block diagram showing a quasi-Moebius monopole antenna.

FIGS. 6A and 6B are views showing input matching characteristics of thequasi-Moebius monopole antenna which is subject to a simulation foroptimization.

FIG. 7 is a view showing surface current distribution for a centerfrequency of the quasi-Moebius monopole antenna at a feeding phase of90°.

FIG. 8 and FIGS. 9A to 9C are views showing two-dimensional radiationpatterns and three-dimensional radiation patterns which are simulatedfor optimization at three frequencies of 3.5 GHz, 4.5 GHz, and 5.5 GHzwithin an operating band of the quasi-Moebius monopole antenna,respectively.

FIG. 10 is a block diagram showing a double circular ring monopoleantenna for miniaturizing a structure of the circular disc monopoleantenna.

FIG. 11 is a graph showing input matching characteristics of circulardisc monopole antennas and type 1 to type 3 antennas.

FIG. 12 is a view showing a simulation of a Moebius strip.

FIG. 13 is a view showing a comparison between the Moebius strip and astrip formed by cutting the Moebius strip along a circumference thereof.

FIGS. 14A and 14B are block diagrams showing a flat Moebius stripaccording to the related art.

FIG. 15 is a front view showing a quasi-Moebius strip.

FIG. 16 is a rear view showing the monopole antenna shown in FIG. 15.

FIG. 17 is a front view showing the quasi-Moebius strip when N=2.

FIGS. 18A and 18B are a front view and a rear view showing thequasi-Moebius strip when N=3, respectively.

FIG. 19 is a front view showing an optimized quasi-Moebius strip.

FIG. 20 is a view showing parameters of the quasi-Moebius strip.

FIG. 21 is a block diagram showing a monopole antenna to which thequasi-Moebius strip is applied.

FIG. 22 is a graph showing a result of simulation for a resonancefrequency and a return loss according to a thickness variation of a ringline.

FIG. 23 is a graph showing a result of measurement for the resonancefrequency and the return loss according to a width variation of abridge.

FIG. 24 is a graph showing a result of comparing return losses of ring1, 2, 3 antennas having mutually different radii with the return loss ofthe quasi-Moebius strip antenna.

FIG. 25 is a view showing a via-hole structure connecting two microstriplines.

FIGS. 26 to 29 are equivalent circuit diagrams of a via-hole.

FIGS. 30A to 30D show examples of inductors implemented on a substrate.

FIGS. 31 and 32 are block diagrams showing first and secondquasi-Moebius strips, respectively.

FIGS. 33 and 34 are block diagrams showing first and secondquasi-Moebius strip antennas, respectively.

FIGS. 35 and 36 are a front view and a rear view showing an antenna towhich a quasi-Moebius strip is applied according to a preferredembodiment of the present invention.

FIG. 37 is a graph showing simulation results in which, when N=1, 2, and3, return losses and resonance frequencies of a first type quasi-Moebiusstrip antenna are compared with each other.

FIG. 38 is a graph in which simulation results of the return loss of theoptimized quasi-Moebius strip antenna are compared with measurementresults thereof.

FIGS. 39A and 39B and FIGS. 40A and 40B are graphs showing measurementresults of radiation patterns of the optimized quasi-Moebius stripantenna and the quasi-Moebius strip antenna, respectively.

FIGS. 41 to 43 are views showing states in which a radiator of a UWBantenna shown in FIG. 35 is rotated by 90°, 180°, and 330°,respectively.

FIGS. 44 to 47 are graphs showing measured return losses of the antennasshown in FIG. 35 and FIGS. 41 to 43, respectively.

FIG. 48 is a graph showing a comparison result of the return lossaccording to the rotation angle of each of the rotated radiators.

FIGS. 49 to 51 are views showing states in which each ring provided onthe radiator of the quasi-Moebius strip is rotated by 300°, 330°, and350°, respectively.

FIGS. 52 to 57 are graphs showing two-dimensional radiation patterns ofthe radiators shown in FIGS. 49 to 51 when φ=0° and 90°.

FIGS. 58 to 60 are graphs showing three-dimensional radiation patternsof the radiators shown in FIGS. 49 to 51, respectively.

BEST MODE Mode for Invention

Hereinafter, a monopole antenna according to a preferred embodiment ofthe present invention will be described in detail with reference to theaccompanying drawings.

1 Miniaturization of Monopole Antenna

FIG. 1 is a block diagram showing a circular disc-shaped monopoleantenna having a coplanar waveguide transmission line (hereinafterreferred to as “CPW TL”) implemented on a dielectric substrate.

Electrical characteristics of the dielectric substrate are expressed bya dielectric constant ε_(r) of a dielectric, a dielectric thickness H, acopper foil thickness T, and a loss tangent value (tan δ). In thisembodiment, the dielectric substrate a dielectric constant ε_(r)=2.2, adielectric thickness H=30 mils (0.762 mm), a copper foil thickness T=0.5oz. (0.018 mm), and a loss tangent value (tan δ)=0.001 (@ 5 GHz) isused.

In a coplanar waveguide line structure, as shown in FIG. 1, values of aslot width S_(g) and a center strip line width W_(f) are varied in a CPWTL feeding structure having strip transmission lines coplanar with twoground planes formed on both sides of a center strip line to adjust adesired characteristic impedance value.

FIGS. 2A to 2C are conceptual diagrams showing surface currentdistribution for each operating frequency of the circular disc monopoleantenna at a feeding phase of 0°.

It can be seen that a surface current flows mainly on an outer peripheryof a circular disc, and the current flows rarely in a center portion ofthe circular disc. Therefore, it is considered that the center portioncan be partially removed to form an annular monopole antenna structure,which will be utilized in further miniaturization studies using amultiple closed-loop monopole antenna structure.

The surface current distributions at 3.0 GHz and 4.5 GHz are directed inan identical direction in a circular disc structure, whereas a radiatorforms higher-order mode current distribution at 6.0 GHz because 6.0 GHzis greater than an operating frequency, so that the radiation pattern ofan azimuth direction may be degraded because the radiation patternhaving a horizontal omni-directional characteristic may be shifted tohave a directivity of slightly offset vertically upward.

The miniaturization of the antenna affects radiation patterncharacteristics such as directivity, gain, and radiation efficiency, sothat careful attention has to be paid during a design process.

FIG. 3 is a block diagram showing a circular double-closed-loop monopoleantenna (hereinafter referred to as “type 1”) for miniaturizing astructure of the circular disc monopole antenna.

The circular double-closed-loop monopole antenna shown in FIG. 3 isdesigned by using a dielectric substrate with a dielectric constantε_(r)=2.2, a dielectric thickness H=30 mils (0.762 mm), a copper foilthickness T=0.5 oz. (0.018 mm), and a loss tangent value (tan δ)=0.001(@ 5 GHz), and has a CPW feeding structure.

Since a size of a CPW feeding unit affects an input impedance and theradiation pattern, the size of the CPW feeding unit is selected to besuitable for a circular double-closed-loop monopole structure.

Optimized design parameters for a structure of the circulardouble-closed-loop monopole antenna are disclosed in Table 1.

TABLE 1 Design Note for Design Design Parameter Parameter Value NoteW_(f) Center strip line width  3.57 mm Determines input L_(f) Centerstrip line length  5.20 mm characteristic S_(g) Slot interval (Interval 0.20 mm impedance between center strip and (No relation to L_(f))ground plane) D Inner diameter of circular 16.00 mm Determines doubleclosed loop impedance, W Width of closed loop line  2.50 mm and relatesto S Interval between loops  0.50 mm impedance- (Slot width) matchingW_(m) Feed matching line width  1.50 mm inductance L_(m) L_(m) Feedmatching length  1.33 mm and capacitance GL GW Ground plane width 24.00mm GL Ground plane length  5.20 mm L₁ Total width of antenna 24.00 mmTotal area of (=0.36 λ_(o)) antenna (λ_(o) is wave- L₂ Total length ofantenna 29.00 mm length at center (=0.44 λ_(o)) frequency) (*)Comparison at a center operating frequency (4.5 GHz)

FIG. 4 is a view showing input matching characteristics of the circulardouble-closed-loop monopole antenna which is subject to a simulation foroptimization.

The input matching characteristics within an operating band are affectedby a size of an outer loop, a line width of a closed loop, a feedmatching length, and a size of a ground plane.

It can be seen that an operating bandwidth is reduced because an antennainput impedance characteristic is degraded at a low-frequency band dueto an attempt to miniaturize a circular double closed loop.

In other words, an input return loss characteristic at a reference of 10dB, which is simulated based on the optimized design parameters in Table1, operates within a band ranging from about 3.6 GHz to 7.3 GHz.

FIG. 5 is a block diagram showing a quasi-Moebius monopole antenna(hereinafter referred to as “type2”), in which design parameters of theantenna and a structure of the quasi-Moebius monopole antenna forminiaturizing the structure of the circular disc monopole antenna areshown.

The quasi-Moebius monopole antenna is designed by using a dielectricsubstrate with a dielectric constant ε_(r)=2.2, a dielectric thicknessH=30 mils (0.762 mm), a copper foil thickness T=0.5 oz. (0.018 mm), anda loss tangent value (tan δ)=0.001 (@ 5 GHz), and has the CPW feedingstructure. Since the size of the CPW feeding unit affects the inputimpedance and the radiation pattern, the size of the CPW feeding unit isselected to be suitable for the structure of the quasi-Moebius monopoleantenna.

Table 2 shows design parameters of the quasi-Moebius monopole antenna,and FIG. 6 is a view showing input matching characteristics of thequasi-Moebius monopole antenna which is subject to a simulation foroptimization.

TABLE 2 Design Design Parameter Note for Design Parameter Value NoteW_(f) Center strip line width  3.57 mm Determines input L_(f) Centerstrip line length  5.53 mm characteristic S_(g) Slot interval (Interval 0.20 mm impedance (No between center strip and relation to L_(f))ground plane) D Inner diameter of circular 16.00 mm Determines doubleclosed loop impedance, and W Width of closed loop line  2.50 mm relatesto impedance- S Interval between loops (Slot  0.50 mm matchinginductance width) L_(m) and W_(m) Feed matching line width  1.54 mmcapacitance GL L_(m) Feed matching length  1.00 mm GW Ground plane width24.00 mm GL Ground plane length  5.53 mm V_(d) Diameter of via-hole 1.00 mm Quasi-Moebius L_(W) Line width of rear surface  1.50 mmconnection line connection line L_(b) Length of rear surface  6.00 mmconnection line L₁ Total width of antenna 24.00 mm Total area of antenna(=0.36 λ_(o)) (λ_(o) is wavelength at L₂ Total length of antenna 29.00mm center frequency) (=0.44 λ_(o))

The input matching characteristics within the operating band areaffected by a size of a quasi-Moebius loop, the line width, a feedmatching length, and the size of the ground plane. The operatingbandwidth is slightly reduced because the antenna input impedancecharacteristic is degraded at the low-frequency band due to an attemptto miniaturize the antenna through quasi-Moebius cross connection.

The input return loss characteristic at the reference of 10 dB, which issimulated based on the optimized design parameters in Table 2, operateswithin a band ranging from about 3.4 GHz to 6.5 GHz.

FIG. 7 is a view showing surface current distribution for a centerfrequency (4.5 GHz) of the quasi-Moebius monopole antenna at a feedingphase of 90°.

It can be seen that the surface current flows mainly on an edge of aquasi-Moebius closed loop, and if a current is determined to be inducedin an identical direction on an inner loop, the structure of themonopole antenna according to the present embodiment is analyzed to beless effective in reducing an antenna resonance length.

FIGS. 8A and 8B and FIGS. 9A to 9C are views showing two-dimensionalradiation patterns and three-dimensional radiation patterns which aresimulated for optimization at three frequencies of 3.5 GHz, 4.5 GHz, and5.5 GHz within the operating band of the quasi-Moebius monopole antenna,respectively.

FIG. 8A shows an azimuth pattern ((p=0°), and FIG. 8B shows an elevationangle pattern ((p=90°).

In addition, Table 3 shows electrical radiation patterns at eachfrequency.

TABLE 3 Operating Frequency Classification 3.5 GHz 4.5 GHz 5.5 GHzAntenna directivity 2.3 dBi 2.8 dBi 3.7 dBi Antenna efficiency(Radiation efficiency + Input matching 91.8% 91.7% 88.8% efficiency)Antenna gain 1.9 dBi 2.4 dBi 3.2 dBi 3-dB beam width 84.4° 79.2° 73.2° @elevation angle

The radiation pattern exhibits excellent characteristics of verticallinearly polarized waves, an antenna gain exhibits an omni-directionalradiation characteristic in a range of about 1.9 dBi within theoperating band, and a characteristic of 8-shaped radiation with a 3-dBbeam width in a range of 73.2° to 84.4° is exhibited at an elevationangle.

FIG. 10 is a block diagram showing a double circular ring monopoleantenna (hereinafter referred to as “type 3”) for miniaturizing thestructure of the circular disc monopole antenna.

As shown in FIG. 10, the double circular ring monopole antenna isdesigned by using a dielectric substrate with a dielectric constantε_(r)=2.2, a dielectric thickness H=30 mils (0.762 mm), a copper foilthickness T=0.5 oz. (0.018 mm), and a loss tangent value (tan δ)=0.001(@ 5 GHz), and has the CPW feeding structure.

Since the size of the CPW feeding unit affects the input impedance andthe radiation pattern, the size of the CPW feeding unit is selected tobe suitable for the structure of the double circular ring monopoleantenna, and Table 4 shows optimized design parameters.

TABLE 4 Design Note for Design Parameter Design Parameter Value NoteW_(f) Center strip line width  0.8 mm Corresponds to L_(f) Center stripline length  4.9 mm 75 Ω input S_(g) Slot interval (Interval  0.20 mmcharacteristic between center strip and impedance ground plane) D₁ Innerdiameter of  4.50 mm Determines circular ring impedance, D₂ Outerdiameter of 16.50 mm and relates to circular ring impedance- d Distancebetween center 10.50 mm matching points of double ring inductance L_(m)S Double ring connection  1.00 mm and capacitance slot width GL L_(m)Feed matching length  1.61 mm GW Ground plane width 19.50 mm GL Groundplane length  5.20 mm L₁ Total width of antenna 19.50 mm Total area of(=0.29 λ_(o)) antenna (λ_(o) is L₂ Total length of antenna 34.50 mmwavelength at (=0.52 λ_(o)) center frequency)

The antenna size (or antenna length) in a lateral direction can bereduced by a double circular ring structure arranged in a longitudinaldirection, which fundamentally allows to provide an excellentomni-directional radiation pattern in the azimuth direction.

As a result of simulating the antenna having the type 3 structure, itcan be confirmed that electric characteristics similar to the inputreturn loss characteristic of the circular disc monopole antenna, whichserves as a reference of the antenna size, can be obtained.

The input return loss characteristic at the reference of 10 dB, which issimulated based on the optimized design parameters, operates within aband ranging from about 2.9 GHz to 6.5 GHz.

FIG. 11 is a graph showing input matching characteristics of circulardisc monopole antennas and type 1 to type 3 antennas.

In the design parameter optimization process, it can be seen that theinput return loss characteristic in a high-frequency band tends to berelatively easy to match, but impedance matching is not smoothlyperformed in a frequency band lower than 3.5 GHz. This generallyindicates that an impedance operating bandwidth is degraded due tominiaturization of the antenna.

FIG. 11 is a view showing two-dimensional radiation patterncharacteristics of compared monopole antenna structures.

Miniaturized structures compared to a reference antenna exhibitrelatively better omni-directional characteristics in the azimuthdirection at the center frequency (4.5 GHz), and a radiation pattern ofa reference antenna structure is similar to radiation patterns of thetype 1 and type 2 structures in the elevation angle (wave angle)direction. However, the type 3 structure is analyzed to exhibitrelatively more directivity because a radiation length is longer in thelongitudinal direction.

Table 5 shows electrical and physical characteristics of the referenceantenna structure in comparison with electrical and physicalcharacteristics of the type 1 to type 3 structures.

TABLE 5 Circular Disc Structure (based Type 1 Type 2 Type 3Classification on physical size) Structure Structure StructureElectrical Operating impedance 2.4~8.0 GHz 3.6~7.3 GHz 3.4~6.5 GHz2.9~6.5 GHz Characteristics bandwidth (based on @ 10 dB) Partialbandwidth ratio 107.7% 67.9% 62.6% 76.6% (%) Antenna directivity^((*))3.3 dBi 2.7 dBi 2.8 dBi 3.1 dBi Antenna efficiency^((*)) 86.8% 92.1%91.7% 92.9% Antenna gain^((*)) 2.7 dBi 2.3 dBi 2.4 dBi 2.7 dBi 3-dB beamwidth^((*)) 72.2° 78.8° 79.2° 71.0° (@ elevation angle) Physical Antennasize 37 × 42 mm 24 × 29 mm 24 × 29 mm 19.5 × 34.5 mm Characteristics(area) (0.55 × 0.63 λ_(o)) (0.36 × 0.44 λ_(o)) (0.36 × 0.44 λ_(o)) (0.29× 0.52 λ_(o)) Miniaturization ratio 100% 44.8% 44.8% 43.3% againstreference (%) ^((*))Comparison at a center operating frequency (4.5 GHz)

Although the miniaturization structure of type 1 to type 3 structureshas a disadvantage in that the operating bandwidth is reduced incomparison with the reference antenna structure, type 1 to type 3miniaturization structures are analyzed to exhibit similar antennadirectivity, antenna efficiency, antenna gains, and 3-dB beam widthcharacteristics, and remarkably effective antenna miniaturization can beachieved with a miniaturization ratio of 42% or less compared to thereference antenna.

2. Quasi-Moebius Monopole Antenna

The Moebius strip has a phase difference of 180° between an inner spaceand an outer space thereof. In other words, the inner space and theouter space are not separated from each other, but are connected to eachother so as to form an open space.

Therefore, the Moebius strip is not divided into two strips when cutalong a circumference thereof, but becomes a single strip having acircumferential length twice as longer as the circumferential length ofthe Moebius strip before the cutting.

In other words, the Moebius strip has no topological beginning and hasone surface. In addition, the Moebius strip is similar to a cylinder,but is a surface having a boundary other than a typical surface.Further, the Moebius strip is not a three-dimensional closed space, buta two-dimensional open space.

Table 6 shows results according to the number of times the Moebius striphas been cut along the circumference.

TABLE 6 Half Twist Number Number of Cuts Result 1 1 1 band length 2 1 22 bands length 2 1 3 3 bands length 2 2 1 2 bands length 1 2 2 3 bandslength 1 2 3 4 bands length 1

When the Moebius strip is twisted once according to the result of Table6, Equations 1 and 2 can be derived as follows.

$\begin{matrix}{{{M( {t,s} )} = {\lbrack {R + {s \cdot {\cos( {\frac{1}{2}t} )}}} \rbrack \cdot {\cos(t)}}},{{{for}\mspace{14mu} 0} \leq t \leq \pi}} & \lbrack {{Equation}\mspace{14mu} 1} \rbrack \\{{{M( {t,s} )} = {\lbrack {R + {s \cdot {\cos( {\frac{1}{2}t} )}}} \rbrack \cdot {\sin(t)}}},{{{for}\mspace{14mu}\pi} \leq t \leq {2\pi}}} & \lbrack {{Equation}\mspace{14mu} 2} \rbrack\end{matrix}$

wherein s∈[−ω, ω], t∈[0,2π], R=the radius of the Moebius strip, andN=Number of cuts of Moebius strip.

The term cos(t) in Equation 1 and the term sin(t) in Equation 2 cause aphase difference of 180°. Therefore, the function M(t, s) indicates thatan end of one side is fixed and rotated by 180° to meet on an oppositeside.

FIG. 12 is a view showing a simulation of a Moebius strip with referenceto Equations 1 and 2.

A total circumferential length l of the Moebius strip can be derived asshown in Equation 3.l=π×(N+1)×R  [Equation 3]

FIG. 13 is a view showing a comparison between the Moebius strip and astrip formed by cutting the Moebius strip along a circumference thereof.

As shown in FIG. 13, the Moebius strip having the inner space and theouter space with a phase difference of 180° can formed into a striphaving a longest circumference when cut along the circumference.

Therefore, the present invention can miniaturize RF passive elementssuch as an antenna, an oscillator, and a resonator by utilizing theabove characteristics of the Moebius strip.

Meanwhile, the applicant has succeeded in miniaturization of themonopole antenna by applying a flat Moebius strip utilizing thecharacteristic of the Moebius strip as disclosed in “MiniaturizedAntenna Using a Planar Moebius Strip Bisected Along The CircumferentialDirection”, IEED Eunc-S. Int. Sym, Proceedings, M. J. Kim, C. S. Cho,and J. Kim, pp. 827-830, October 2006, etc. However, various problemsare caused due to an imperfect structure of the flat Moebius strip.

FIGS. 14A and 14B are block diagrams showing a flat Moebius stripaccording to the related art.

As shown in FIG. 14, a three-dimensional connection bridge at a portionwhere two rings are connected to each other causes a line couplingeffect at a low frequency, so that the three-dimensional connectionbridge is not suitable for application to an RF circuit having a singleresonance frequency characteristic. In addition, the flat Moebius stripaccording to the related art does not have a perfect two-dimensionalstructure, but has a three-dimensional structure, so that there is alimitation in applying the flat Moebius strip to an integrated circuitsuch as a monolithic microwave integrated circuit (MMIC).

In other words, the flat Moebius strip according to the related art hasa three-dimensional bridge for connecting the inner space to the outerspace, which causes an electromagnetic interference, so that it isdifficult to apply the flat Moebius strip to an RF passive elementhaving a single resonance frequency characteristic.

Accordingly, the present invention provides a monopole antenna to whicha quasi-Moebius strip having a via-hole structure is applied in order tominimize a line coupling effect due to structural characteristics of theflat Moebius strip according to the related art and to maximizeminiaturization.

In other words, the present invention maintains the same physical lengthof the Moebius strip while increasing the number of times the Moebiusstrip is cut along the circumference for the purpose of miniaturization.

In this case, a total circumferential length of the Moebius strip cutalong the circumference is twice the circumferential length of thetypical Moebius strip.

In addition, when the quasi-Moebius strip cut along the circumference isapplied to an RF circuit design, the total circumferential length can beshortened while maintaining the resonance frequency.

FIG. 15 is a front view showing a quasi-Moebius strip, and FIG. 16 is arear view showing the monopole antenna shown in FIG. 15.

As shown in FIGS. 15 and 16, the quasi-Moebius strip includes: aradiator arranged on a center of a front surface of a dielectricsubstrate, and including a plurality of loops formed in a structure inwhich the quasi-Moebius strip is cut at least one time along acircumference; a first bridge for sequentially connecting one end ofeach of the loops; and a second bridge for connecting via-holesrespectively formed at one end of an innermost loop and an outermostloop.

In other words, in order to minimize the line coupling effect, which isa problem of the flat Moebius strip according to the related art, thebridges connecting the inner space and the outer space where the tworings intersect with each other are physically separated into front andrear surfaces of the substrate, and connected to each other by thevia-holes.

As the quasi-Moebius strip structure is applied, the present inventioncan minimize the line coupling effect at a low frequency and theelectromagnetic interference that may occur severely as the RF circuitis miniaturized at an identical resonance frequency.

The quasi-Moebius strip may be derived as shown in Equations 4 and 5when N is an even number.

$\begin{matrix}{{{M( {t,s} )} = {\lbrack {R + {s \cdot {\cos( {\frac{1}{2}t} )}}} \rbrack \cdot {\cos(t)}}},{{{for}\mspace{14mu} 0} \leq t \leq \pi},\ldots\mspace{11mu},{{2N\;\pi} \leq t \leq {( {{2N} + 1} )\pi}}} & \lbrack {{Equation}\mspace{14mu} 4} \rbrack \\{{{M( {t,s} )} = {\lbrack {R + {s \cdot {\cos( {\frac{1}{2}t} )}}} \rbrack \cdot {\sin( {t + {N \times \frac{1}{2}\pi}} )}}},\;{{{for}\mspace{14mu}\pi} \leq t \leq {2\pi}},\ldots\mspace{11mu},{{( {{2N}\; + 1} )\pi} \leq t \leq {2( {N + 1} )\pi}}} & \lbrack {{Equation}\mspace{14mu} 5} \rbrack\end{matrix}$

wherein s∈[−ω∩], t∈[0, 2(N+1)π], R=Radius of the Quasi-Moebius strip,and N=Number of cuts of the Quasi-Moebius strip.

Meanwhile, the quasi-Moebius strip may be derived as shown in Equations6 and 7 when N is an odd number.

$\begin{matrix}{{{M( {t,s} )} = {\lbrack {R + {s \cdot {\cos( {\frac{1}{2}t} )}}} \rbrack \cdot {\cos(t)}}},{{{for}\mspace{14mu} 0} \leq t \leq \pi},\ldots\mspace{11mu},{{2N\;\pi} \leq t \leq {( {{2N} + 1} )\pi}}} & \lbrack {{Equation}\mspace{14mu} 6} \rbrack \\{{{M( {t,s} )} = {\lbrack {R + {s \cdot {\cos( {\frac{1}{2}t} )}}} \rbrack \cdot {\sin( {t + {N \times \frac{1}{2}\pi}} )}}},\;{{{for}\mspace{14mu}\pi} \leq t \leq {2\pi}},\ldots\mspace{11mu},{{( {{2N}\; + 1} )\pi} \leq t \leq {2( {N + 1} )\pi}}} & \lbrack {{Equation}\mspace{14mu} 7} \rbrack\end{matrix}$

In addition, the quasi-Moebius strip may be derived as shown inEquations 8 and 9 when N=2.

$\begin{matrix}{{{M( {t,s} )} = {\lbrack {R + {s \cdot {\cos( {\frac{1}{2}t} )}}} \rbrack \cdot {\cos(t)}}},{{{f{or}}\mspace{14mu} 0} \leq t \leq \pi},\ldots\mspace{11mu},{{4\;\pi} \leq t \leq {5\pi}}} & \lbrack {{Equation}\mspace{14mu} 8} \rbrack \\{{{M( {t,s} )} = {\lbrack {R + {s \cdot {\cos( {\frac{1}{2}t} )}}} \rbrack \cdot {\sin( {t + {N \times \frac{1}{2}\pi}} )}}},\;{{{for}\mspace{14mu}\pi} \leq t \leq {2\pi}},\ldots\mspace{11mu},{{5\pi} \leq t \leq {6\;\pi}}} & \lbrack {{Equation}\mspace{14mu} 9} \rbrack\end{matrix}$

FIG. 17 is a front view showing the quasi-Moebius strip when N=2.

As described above, when the number N of cutting the quasi-Moebius stripalong the circumference thereof is increased, it can be seen that thetotal circumferential length is increased by (N+1) times. Therefore, theminiaturization of the quasi-Moebius strip can be achieved by increasingN under a condition of the identical resonance frequency.

Accordingly, in this embodiment, miniaturized circuits and systems canbe designed at the identical resonance frequency by applying thequasi-Moebius strip in which N is increased to the RF circuit design.

In this embodiment, when the phase difference between the inner spaceand the outer space of the quasi-Moebius strip is 180°, thequasi-Moebius strip can be miniaturized by increasing the number N ofcutting the quasi-Moebius strip along the circumference.

In addition, FIGS. 18A and 18B are a front view and a rear view showingthe quasi-Moebius strip when N=3, respectively.

When N=3, the total circumferential length becomes 87c, and anodd-numbered ring and an even-numbered ring are designed in a flat shapeon the substrate with the phase difference of 180°.

As shown in FIGS. 18A and 18B, in order to minimize the electromagneticinterference, a connection bridge for a ring 1 and a ring 4 are designedon the front surface of the substrate, connection bridges for the ring 1and a ring 2, the ring 2 and a ring 3, and the ring 3 and the ring 4 aredesigned on the front surface of the substrate and connected to eachother by the via-holes.

3. Impedance Matching of Quasi-Moebius Strip by Parameter Sweep

When the number N of cutting the quasi-Moebius strip along thecircumference thereof is increased, the total circumferential length isincreased by (N+1) times, so that the miniaturization can be achieved byincreasing N of the quasi-Moebius strip.

The quasi-Moebius strip having the via-hole structure does not resonatewith a designed resonance frequency without optimization of a positionof the via-hole and the structure of the quasi-Moebius strip.

Hereinafter, an impedance matching process optimized for a designedresonance frequency through a parameter sweep will be described based onvariations in the position and a size of the via-hole of thequasi-Moebius strip having the via-hole structure, and a thickness of aring of the quasi-Moebius strip, and the width of the bridge.

Three parameters of the parameter sweep for the impedance matching ofthe quasi-Moebius strip are a thickness of a ring line of thequasi-Moebius strip, the width of the bridge, and a variation in theposition and a radius of the via-hole.

Therefore, a process in which the resonance frequency and the impedancematching vary will be described as the thickness of the ring line of thequasi-Moebius strip is changed among the three parameters.

Table 7 shows the resonance frequency and a return loss according to avariation in the thickness of the ring line of the quasi-Moebius strip,FIG. 19 is a front view showing an optimized quasi-Moebius strip, andFIG. 20 is a view showing parameters of the quasi-Moebius strip.

TABLE 7 Thickness of ring line Primary Helical line Thickness resonancenumber (1, 2, 3) (mm) frequency (GHz) S₁₁(dB) 1, 2, 3 0.6 2.430 −15.3501, 2, 3 0.7 2.430 −15.210 1, 2, 3 0.8 2.430 −15.416 1, 2, 3 0.9 2.440−16.181 1, 2, 3 1 2.505 −17.550 3 1 2.415 −15.151 1, 2 0.6 1 1 2.455−16.211 2, 3 0.6 2 1 2.340 −13.405 1, 3 0.6 1 0.6 2.720 −28.006 2, 3 1 20.6 2.49 −17.0226 1, 3 1 3 0.6 2.435 −15.6295 1, 2 1

As disclosed in Table 7, the thickness of the ring line having a bestreturn loss characteristic while approaching to the designed resonancefrequency of 2.4 GHz is achieved when ring lines 1 and 3 have athickness of 1 mm, and a ring line 2 has a thickness of 0.6 mm.

FIG. 21 is a block diagram showing a monopole antenna to which thequasi-Moebius strip is applied.

As shown in FIG. 21, a monopole antenna to which the quasi-Moebius stripis applied can be optimized by varying the three parameters of theMoebius strip, that is, the thickness of the ring line, the width of thebridge, and the position and radius of the via-hole.

FIG. 22 is a graph showing a result of simulation for a resonancefrequency and a return loss according to a thickness variation of a ringline.

Next, a process of optimizing the resonance frequency and the impedancematching by varying the position and radius of the via-hole of thequasi-Moebius strip among the three parameters of the quasi-Moebiusstrip will be described.

The thickness of the ring line of the quasi-Moebius strip is optimizedwhen the thickness of the ring lines 1 and 3 is 1 mm in, and thethickness of the ring line 2 is 0.6 mm.

Therefore, the optimization can be achieved by varying the position andthe radius of the via-hole under the above conditions.

Table 8 shows the resonance frequency and the return loss according tothe variation in the position and radius of the via-holes of thequasi-Moebius strip.

TABLE 8 Position and radius of via-hole Resonance Position Radius (mm)frequency (GHz) S₁₁(dB) center 0.5(H) 2.445 −15.348 center 0.5(L) center0.8(H) 2.460 −15.94 center 0.8(L) center   1(H) 2.475 −16.92 center  1(L) center 0.5(H) 2.490 −17.023 center   1(L) center   1(H) 2.445−15.436 center 0.5(L) edge 0.5(H) 2.450 −15.9027 edge 0.5(L) edge 0.8(H)2.465 −16.66 edge 0.8(L) edge   1(H) 2.490 −17.15 edge   1(L) edge0.5(H) 2.470 −16.631 edge   1(L) edge   1(H) 2.470 −16.51 edge 0.5(L)

As disclosed in Table 8, the position and radius of the via-hole havingthe best return loss characteristic while approaching to the designedresonance frequency of 2.4 GHz are achieved when a via-hole located onan upper side about a y axis has a radius of 0.5 mm, and a via-holelocated on a lower side has a radius of 1 mm.

Next, a process of optimizing the resonance frequency and the impedancematching by varying the width of the bridge among the three parametersof the quasi-Moebius strip will be described.

The resonance frequency and the return loss can be optimized by varyingthe width of the bridge of the quasi-Moebius strip under the conditionof the optimized thickness of the ring line, and the optimized positionand radius of the via-hole of the quasi-Moebius strip.

Table 9 shows the resonance frequency and the return loss according to awidth variation of the bridge, and FIG. 23 is a graph showing a resultof measurement for the resonance frequency and the return loss accordingto the width variation of the bridge.

TABLE 9 Position and area of bridge Primary resonance Position Area (mm)frequency (GHz) S₁₁ (dB) center 0 2.495 −17.21  center +0.5 2.490−17.2663 center 1 2.490 −17.0826 center 1.5 2.485 −17.1833 center 22.475 −17.079  center −0.25 2.495 −17.2586

According to Table 9, the width of the bridge having an excellent returnloss characteristic while approaching to the designed resonancefrequency of 2.4 GHz is achieved when the width of the bridge is about0.5 mm wide as shown in FIG. 23.

Finally, it is possible to design an optimized quasi-Moebius strip withthe excellent return loss characteristic while approaching to thedesigned resonance frequency of 2.4 GHz by varying the three parametersof the quasi-Moebius strip.

According to the simulation results, it is confirmed that the returnloss of the quasi-Moebius strip is optimized when the thickness of thering lines 1 and 3 is 1 mm, the thickness of the ring line 2 is 0.6 mm,the via-hole located on the upper side about the y axis has the radiusof 0.5 mm, and the via-hole located on the lower side has the radius of1 mm.

Finally, the width of the bridge of the quasi-Moebius strip is optimizedwhen the width of the bridge is about 0.5 mm wide.

Meanwhile, it is confirmed from the simulation results that ringantennas having three modified ring lines constituting the quasi-Moebiusstrip and having mutually different radii do not form the resonantfrequency.

FIG. 24 is a graph showing a result of comparing return losses of ring1, 2, 3 antennas having mutually different radii with the return loss ofthe quasi-Moebius strip antenna.

According to the simulation result, the resonance frequency of thequasi-Moebius strip antenna is formed in the 2.4 GHz band, and the peakvalue of the return loss (S11) is 17.3 dB.

According to simulation and measurement results, the antenna appliedwith the quasi-Moebius strip optimized in the present embodiment isformed of three ring lines having mutually different radii, but has acharacteristic of a single resonant frequency.

In addition, when compared with the conventional ring antenna having thesame resonance frequency, the size of the antenna applied with thequasi-Moebius strip is miniaturized to about ⅓.

4. Via-Hole Equivalent Circuit

FIG. 25 is a view showing a via-hole structure connecting twomicro-strip lines.

As shown in FIG. 25, the via-hole may be formed of two pads and onecylinder.

The complicate via-hole equivalent circuit can be simplified dependingon the frequency and the bandwidth, and FIG. 26 is an equivalent circuitdiagram of the most accurate but complex via-hole.

The equivalent circuit shown in FIG. 26 includes three distributedconstant elements in a lossless transmission line. The three elementsare an upper pad, a cylinder, and a lower pad, and there is a couplingcapacitance between the elements. The mutual capacitance C between theelements exists between conductor elements. In addition, in theequivalent circuit shown in FIG. 26, the mutual inductance M is alsopresent.

The mutual inductance M is generated by a magnetic flux generated by achange of a magnetic field according to the time between the coupledconductor elements. The equivalent circuit can be applied accuratelyregardless of the frequency, but the circuit is complicated and thesimulation time may be long.

FIG. 27 is a distributed constant via equivalent circuit diagram whichcan be practically applied as compared with FIG. 26.

In FIG. 27, as the frequency becomes higher, there is a clear influencebetween the respective elements. As the diameter of the cylinder of thevia-hole decreases, the upper pad and the lower pad become capacitiveand the cylinder becomes inductive.

Therefore, the distributed constant via equivalent circuit shown in FIG.27 excludes a coupling phenomenon between the respective elements, sothat it is difficult to accurately apply the distributed constant viaequivalent circuit at high frequencies.

FIG. 28 is a lumped via equivalent circuit diagram.

The via-hole equivalent circuit shown in FIG. 28 is the simplest amongthe three via equivalent circuits, and can be practically applied whenthe resonance frequency is less than 3.5 GHz.

In the via-hole equivalent circuit, since the size of the via-hole isrelatively small compared to the wave length at the low frequency, theenergy radiated from the via-hole can be ignored. Therefore, thevia-hole is interpreted as a lumped element.

However, in the high frequency, there is a strong interaction betweenthe magnetic and electrical energies, resulting in non-negligibleelectromagnetic radiation. Therefore, the via-hole is interpreted as afull wave method or a n-type equivalent circuit including L (Inductor)and C (Capacitor).

When the target frequency is 2.4 GHz, since 2.4 GHz is a relatively lowfrequency, the via-hole is interpreted as a lumped element.

FIG. 29 is a via-hole equivalent circuit applied in this embodiment.

One via-hole is connected to one inductance L connected in series andtwo capacitances C connected in parallel. It can be deduced that theequivalent circuit of the entire quasi-Moebius strip varies depending onthe radius and position of the via-hole from the via-hole equivalentcircuit.

Meanwhile, the quasi-Moebius strip is formed of an inductance Lcomponent and a capacitance C component which increase according to thenumber of times of cutting.

The quasi-Moebius strip includes n ring lines and bridges.

FIGS. 30A to 30D show examples of inductors implemented on a substrateand Table 10 is a coefficient current sheet of an inductance L.

According to Table 10, since the shape of the ring line of thequasi-Moebius strip according to the present embodiment is a circleshape, c1, c2, c3, and c4 are 1.00, 2.46, 0.00, and 0.20, respectively.

TABLE 10 Layout c₁ c₂ c₃ c₄ Square 1.27 2.07 0.18 0.13 Hexagonal 1.092.23 0.00 0.17 Octagonal 1.07 2.29 0.00 0.19 Circle 1.00 2.46 0.00 0.20

The impedance matching condition is obtained when the relationshipbetween the characteristic impedance Z₀ and the load impedance Z_(L) isa complex conjugate.

That is, to find L and C that meet the impedance matching condition ofthe quasi-Moebius strip antenna according to the present embodiment, itis necessary to derive L and C that satisfy the relation Z₀=Z_(L)*,where Z₀=characteristic impedance=50Ω and Z_(L)=load impedance.

The total inductance L and the total capacitance C of the quasi-Moebiusstrip antenna are derived as shown in Equation (10) and Equation (11).

$\begin{matrix}{{L_{total} = {{\sum\limits_{i = 0}^{M}L_{i + 1}} \approx {\frac{\mu_{0}M^{2}d_{avg}c_{1}}{2}\lbrack {{\ln( \frac{c_{2}}{\rho} )} + {c_{3}\rho} + {c_{4}\rho^{2}}} \rbrack}}},\mspace{20mu}{\rho = \frac{d_{out} - d_{inner}}{d_{out} + d_{inner}}}} & \lbrack {{Equation}\mspace{14mu} 10} \rbrack \\\begin{matrix}{\mspace{79mu}{{C_{total} = {\sum\limits_{i = 0}^{M}\frac{1}{C_{i}}}},}} & {C_{i} = {{ɛ\frac{A}{H}} = {ɛ\frac{W \cdot L}{H}}}}\end{matrix} & \lbrack {{Equation}\mspace{14mu} 11} \rbrack\end{matrix}$

wherein W=longitudinal length (m) of conductor, L=transverse length (m)of conductor, and H=interval (m) between upper conductor and lowerconductor.

Hereinafter, the equivalent circuit of the quasi-Moebius strip antennawill be explained by using the total L and C satisfying the impedancematching condition of the quasi-Moebius strip antenna derived fromEquations (10) and (11), and the simulation results will be compared andanalyzed to represent different points.

FIGS. 31 and 32 are block diagrams showing first and secondquasi-Moebius strips (hereinafter referred to as “first type and secondtype”), respectively.

The first type quasi-Moebius strip is implemented as an open strip thatis connected without the beginning and the end, which is thecharacteristic of the Moebius strip, by forming ring lines 1, 2, 3 byrotating ring lines having mutually different radii from 0° to 325° andconnecting the ring lines 1, 2, 3 to each other at the front and rearsurfaces of the substrate. That is, the first type quasi-Moebius stripis formed by connecting the ring line 1 having a radius of 3 mm to thering line 2 having a radius of 3.75 and connecting the ring line 3having a radius of 4.5 mm to the ring line 2 at the front surface of thesubstrate. In addition, the ring line 1 is connected to the ring line 3via the bridge 1 at the rear surface of the substrate.

The second type quasi-Moebius strip is implemented as an open strip thatis connected without the beginning and the end, which is thecharacteristic of the Moebius strip, by forming ring lines 1, 2, 3 byrotating ring lines having mutually different radii from 0° to 325° andconnecting the ring line 1 to the ring line 3 at the front surface ofthe substrate and connecting the ring line 1 to the ring line 2 andconnecting the ring line 2 to the ring line 3 at the rear surface of thesubstrate.

FIGS. 33 and 34 are block diagrams showing first and secondquasi-Moebius strip antennas, respectively.

When N=2, the antenna to which the first type quasi-Moebius strip isapplied has one bridge and two via-holes. The antenna to which thesecond type quasi-Moebius strip is applied has two bridges and fourvia-holes.

That is, since the C and L components of the equivalent circuit varydepending on the number of via-holes and the number of bridges, theequivalent circuit of the antenna to which the first type quasi-Moebiusstrip is applied is different from the equivalent circuit of the antennato which the second type quasi-Moebius strip is applied.

According to the simulation result, the difference in the return losscharacteristic proportionally increases as the first type quasi-Moebiusstrip antenna and the second type quasi-Moebius strip antenna areminiaturized (as N increases).

Particularly, according to the simulation result obtained when N=3, thefirst type quasi-Moebius strip antenna has a wide bandwidth of about 1.5GHz to 5 GHz based on −10 dB. However, the resonance frequency rarelyoccurs in the second type quasi-Moebius strip antenna.

Accordingly, the first type quasi-Moebius strip antenna is applied tothe present invention.

FIGS. 35 and 36 are a front view and a rear view showing an antenna towhich a quasi-Moebius strip is applied according to a preferredembodiment of the present invention.

In the quasi-Moebius strip according to the preferred embodiment of thepresent invention, as shown in FIGS. 35 and 36, when N=3, the ring 1 andthe ring 4 are connected to each other through the bridge 1, the ring 3and the ring 4 are connected to each other through the bridge 2, thering 2 and the ring 3 are connected to each other through the bridge 3,and the ring 1 and the ring 2 are connected to each other through thebridge 4.

In order to increase the miniaturization effect in the presentembodiment, the distance of the ring 1, the ring 2, the ring 3, and thering 4 may be set to a radius r, 1.68 mm, which is 0.5 times of 3.36 mm.

In addition, in order to minimize the electromagnetic wave interferencephenomenon and increase the miniaturization effect in the presentembodiment, the bridge 1 may be provided on the rear surface of thesubstrate, and the bridge 2, the bridge 3, and the bridge 4 may beprovided on the front surface of the substrate.

However, the present invention is not limited thereto, and the bridge 1may be provided on the front surface of the substrate, and the bridge 2to the bridge 4 may be provided on the rear surface of the substrate.

As the antenna using the quasi-Moebius strip described in the presentembodiment is miniaturized, that is, as the N (number of cuts)increases, the number of rings (=helical lines) constituting thequasi-Moebius strip, the number of bridges, and the number of via-holesincrease proportionally.

That is, as the antenna to which the quasi-Moebius strip is applied isminiaturized, the equivalent circuit is changed due to the change andincrease of the inductance L and the capacitance C, so the correspondingimpedance matching method can be applied.

5. Simulation and Measurement Results

FIG. 37 is a graph showing the simulation results in which, when N=1, 2,and 3, return losses and resonance frequencies of a first typequasi-Moebius strip antenna are compared with each other.

The simulation results show that as the quasi-Moebius strip antenna isminiaturized, the return loss characteristic deteriorates, the linecoupling effect increases, and the resonance frequency increases.

That is, as the number of N of the quasi-Moebius strip increases, animpedance matching method and a procedure to be applied to aminiaturized quasi-Moebius strip antenna are required.

Accordingly, there is a need to perform an impedance matching processoptimized for the resonance frequency, which is designed through theparameter sweep according to the position and size of the via-hole ofthe quasi-Moebius strip, the ring line thickness of the quasi-Moebiusstrip, and the size of the bridge.

FIG. 38 is a graph in which simulation results of the return loss of theoptimized quasi-Moebius strip antenna are compared with measurementresults thereof.

Referring to FIG. 38, when compared to the simulation result, theresonance frequency is shifted toward about 300 MHz, and the reflectioncoefficient is sharply dropped to 27 dB.

The resonance frequency designed in the present embodiment is 2.4 GHz,but the actual resonance frequency according to the measurement resultof FIG. 38 is 2.78 GHz, so the radiation pattern was measured at 2.4GHz, 2.5 GHz and 2.78 GHz.

FIGS. 39A and 39B and FIGS. 40A and 40B are graphs showing measurementresults of radiation patterns of the optimized quasi-Moebius stripantenna and the quasi-Moebius strip antenna (N=1), respectively.

In FIG. 39, the omni-directional characteristics can be confirmed atfrequencies of 2.5 GHz and 2.78 GHz when φ=90° similar to a far-fieldmonopole antenna.

In FIG. 40, the omni-directional characteristics can be confirmed atfrequencies of 2.5 GHz, 2.42 GHz and 2.43 GHz when φ=90° similar to afar-field monopole antenna.

Especially, when comparing FIG. 39 with FIG. 40, the peak gain and theaverage gain of the radiation pattern increase at the resonancefrequency of 2.78 GHz as shown in Table 11 even when the miniaturizationis achieved due to the increase of N.

TABLE 11 N = 1 N = 2 Peak Average Peak Average Frequency Gain Gain GainGain (GHz) (dBd) (dBd) Frequency (dBd) (dBd) 2.4 1.99 −3.94 2.4 −2.36−8.20 2.42 2.17 −4.16 2.5 −1.14 −5.00 2.43 2.68 −3.62 2.78 2.93 −3.35

That is, even if the quasi-Moebius strip antenna is miniaturized, thereflection coefficient and the gain can be optimized by varying the ringline thickness, the position and the radius of the via-hole, and thewidth of the bridge.

5. Quality Factor and Bandwidth Control

FIGS. 41 to 43 are views showing states in which a radiator of a UWBantenna shown in FIG. 35 is rotated by 90°, 180°, and 330°,respectively.

FIGS. 44 to 47 are graphs showing measured return losses of the antennasshown in FIG. 35 and FIGS. 41 to 43, respectively.

FIG. 48 is a graph showing a comparison result of the return lossaccording to the rotation angle of each of the rotated radiators.

As can be seen from the drawings showing the measurement of return loss,the present invention can control the Q factor and bandwidth by rotatingthe radiator of the quasi-Moebius strip antenna.

6. Directivity Control

The present invention can control the directivity by adjusting therotation angle of each ring provided on the radiator of thequasi-Moebius strip.

For example, FIGS. 49 to 51 are views showing states in which each ringprovided on the radiator of the quasi-Moebius strip is rotated by 300°,330°, and 350°, respectively.

FIGS. 52 to 57 are graphs showing two-dimensional radiation patterns ofthe radiators shown in FIGS. 49 to 51 when φ=0° and 90°.

In addition, FIGS. 58 to 60 are graphs showing three-dimensionalradiation patterns of the radiators shown in FIGS. 49 to 51,respectively.

That is, the present invention can control the directivity of theradiation pattern of the antenna by adjusting the rotation angle of eachring provided in the radiator of the quasi-Moebius strip to between 0°to 360°.

In detail, as the rotation angle of the ring approaches to 360°, theradiation pattern has the omni-directional characteristic, and thedirectivity is increased as the rotation angle becomes small.

That is, as the rotation angle of the ring approaches to 360°, theradiation pattern characteristic is similar to that of the circular discmonopole antenna.

The radiation pattern of the circular disc monopole antenna has theomni-directional characteristic. This is because the directivity isdetermined based on the distribution of the electric field and magneticfield according to the current feeding.

Therefore, the quasi-Moebius strip antenna according to the presentinvention represents the omni-directional characteristic as the rotationangle of the ring provided on the radiator approaches to 360°, and thedirectivity is increased as the rotation angle of the ring becomessmall.

7. Small MIMO Antenna Using Monopole Antenna

The MIMO antenna is a core of 4G and 5G technologies and is applied toovercome the limitation of the channel capacity caused by multipathfading. By applying a plurality of transmitting and receiving antennasto the end of the transmitting and receiving terminals, the limitationof the channel capacity caused by the multipath is improved.

The performance parameters of the MIMO antenna are mainly divided into adiversity performance and a MIMO performance. Diversity performanceparameters include balanced branch power mean gain (MEG), correlation,and diversity gain, and MIMO performance parameters include MIMOcapacity and multiplexing efficiency.

In the MIMO system, the channel capacity increases in proportion to thenumber of transmitting and receiving antennas, but there is acorrelation between the antennas because a plurality of antennas areused. The correlation between the antennas reduces the channel capacityof the entire MIMO system. When designing the MIMO antenna, a diversitytechnique that improves spectral efficiency is adopted and the mutualcoupling relationship between antennas degrades the performance of thesystem.

The correlation between the MIMO antennas is one of the most importantparameters related to the spectral efficiency of the communicationsystem, and the spectral efficiency of the communication system isdegraded as the correlation between the antennas becomes high.

The calculation of the envelope correlation coefficient (ECC), which isthe correlation between the antennas, can be defined by Equation 12 or13 in consideration of the three-dimensional radiation pattern.

$\begin{matrix}\frac{\rho_{e} = {{\int_{4\;\pi}^{\;}{\int{\lbrack {{\overset{\_}{F_{1}}( {\theta,\phi} )} \cdot {{\overset{\_}{F}}_{2}^{*}( {\theta,\phi} )}} \rbrack d\;\Omega}}}}^{2}}{\int_{4\;\pi}^{\;}{\int{{{{\overset{\_}{F}}_{1}( {\theta,\phi} )}}^{2}d\;\Omega{\int_{4\;\pi}^{\;}{\int{{{\overset{\_}{F_{2}}( {\theta,\phi} )}}^{2}d\;\Omega}}}}}} & \lbrack {{Equation}\mspace{14mu} 12} \rbrack\end{matrix}$

wherein, F_(i)(θ, φ) denotes a radiation pattern obtained only when I isexcited in a case that all other ports are terminated to 50Ω and •denotes Hermitian operation.

$\begin{matrix}{\rho_{e} = ( \frac{\oint{( {{{{XPR} \cdot E_{\theta\; X}}E_{\theta\; X}^{*}P_{\theta}} + {E_{\phi\; Y}E_{\phi\; Y}^{*}P_{\phi}}} )d\;\Omega}}{\;\sqrt{\begin{matrix}{\oint{( {{{{XPR} \cdot E_{\theta\; X}}E_{\theta\; X}^{*}P_{\theta}} + {E_{\phi\; X}E_{\phi\; X}^{*}P_{\phi}}} )d\;\Omega}} \\{\oint{( {{{XPR} \cdot E_{\theta\; Y}}E_{\theta\; Y}^{*}P_{\phi}} )d\;\Omega}}\end{matrix}}} )^{2}} & \lbrack {{Equation}\mspace{14mu} 13} \rbrack\end{matrix}$

wherein, XPR=cross polarization ratio=Pθ(Ω)/Pφ(Ω), E_(θ,φ)X and E_(θ,φ)denote the crossed electric field pattern between two antennas of aplurality of antennas.

Equation 12 can be expressed in a simplified form by using anS-parameter between array antennas. If the environment of the multipathis uniform, Equation 12 can be approximated by Equation 14.

$\begin{matrix}{\rho_{e} = \frac{{{{S_{11}^{*}S_{12}} + {S_{21}^{*}S_{22}}}}^{2}}{( {1 - {S_{11}}^{2} - {S_{21}}^{2}} )( {1 - {S_{22}}^{2} - {S_{12}}^{2}} )}} & \lbrack {{Equation}\mspace{14mu} 14} \rbrack\end{matrix}$

Equation 14 is derived by applying an S parameter between two antennasto derive an ECC, which is simpler than the calculation using Equation13.

Meanwhile, the next generation wireless communication requires a highcapacity MIMO antenna technology for high speed data transmission. Inorder to realize the high capacity MIMO antenna having the highisolation characteristics, a plurality of highly isolated antennasshould be implemented in a limited radiation space.

To this end, a small MIMO antenna geometry with two antenna terminalshaving the same radiator structure may be considered.

Since the antenna terminals are very close to each other, the signalsoutput to a mating terminal through a long path and a short path maysatisfy the phase conjugate condition, that is, the 180° phasedifference condition, at the same amplitude, so that the terminalisolation characteristics may be satisfied.

This can be achieved by appropriately adjusting a diameter of a circulardisc and a width S1 and a length S2 of a slot implemented in thecircular disc.

The structure (width and length) of the slot may exert an influence onan input impedance and terminal isolation characteristics of theantenna.

The optimized design is achieved by using a dielectric substrate with adielectric constant ε_(r)=2.2, a dielectric thickness H=30 mils (0.762mm), a copper foil thickness T=0.5 oz. (0.018 mm), and a loss tangentvalue (tan δ)=0.001 (@ 5 GHz). In order to easily implement the inputimpedance matching circuit, the micro-strip feeding was used instead ofthe CPW feeding. In addition, each input terminal is implemented at a 1mm offset position from the slot.

When the input return loss characteristics and the terminal isolationcharacteristics are considered on the basis of 10 dB, it can operate inthe 3.33 GHz˜5.67 GHz band. Especially, in the 3.2˜5.0 GHz band,excellent input matching characteristics having the input reflectioncoefficient of 0.18 or less and superior isolation characteristics canbe represented.

The simulation result shows that a wideband 2-terminal small MIMOantenna with high isolation characteristics can be implemented in aspace of about 0.54λ_(o)×0.69λ_(o).

The signal input from each terminal appears weakly to the counterterminal due to the slot structure. As can be understood from theterminal isolation characteristics shown in a picture 3.4.3 (a), theterminal isolation characteristic in the 5.5 GHz band is about 11.3 dB,which is not better than 22 dB to 28 dB in the other frequency band (3.5GHz & 4.5 GHz), so it is confirmed that the counter signals are stronglycoupled relatively.

In addition, the two-terminal small MIMO antenna described in thepresent embodiment has a very low correlation between antennas within afrequency range of 3 GHz to 8 GHz, and can be utilized for a massiveMIMO antenna for UWB.

As described above, when the miniaturized UWB antenna according to thepresent embodiment is applied to the MIMO antenna, it is confirmed thatthe ECC value indicating the correlation between the antennas is 0.02 orless in the frequency range of 3 GHz to 8 GHz, thereby improving thespectral efficiency.

Although the invention made by the present inventors has been describedconcretely with reference to the above embodiments, the presentinvention is not limited to the above embodiments, and various changescan be made without departing from the scope of the present invention.

That is, although the UWB monopole antenna has been described in theabove embodiments, the present invention is not limited thereto. Thepresent invention can be applied to various types of monopole antennasas well as UWB monopole antennas, and can be applied to an RF passiveelement, such as a resonant cell, wireless power transmission resonator,an oscillator, and the like.

INDUSTRIAL APPLICABILITY

The present invention may be applied to a monopole antenna techniqueadopting a quasi-Moebius strip structure.

The invention claimed is:
 1. A monopole antenna comprising: a radiatorarranged on a center of a front surface of a dielectric substrate, andincluding a plurality of loops formed in a structure in which aquasi-Moebius strip is cut at least one time along a circumference; afirst bridge for sequentially connecting one end of each of the loops;and a second bridge for connecting via-holes respectively formed at oneend of an innermost loop and an outermost loop, wherein the antenna isminiaturized through a combination of the radiator, the first bridge andthe second bridge, each of the loops of the radiator is provided withring lines having diameters different from each other, and the monopoleantenna has a single resonance frequency characteristic.
 2. The monopoleantenna of claim 1, wherein the first bridge is disposed on the frontsurface of the dielectric substrate, and the second bridge is disposedon a rear surface of the dielectric substrate.
 3. The monopole antennaof claim 2, wherein a Q-factor (Quality factor) and a bandwidth arecontrollable by adjusting a rotation angle of the radiator.
 4. Themonopole antenna of claim 3, wherein directivity is controllable byadjusting a rotation angle of each of the loops provided in theradiator.
 5. The monopole antenna of claim 4, wherein the monopoleantenna has an omni-directional characteristic as the rotation angle ofeach of the loops approaches to 360°, and the directivity is increasedas the rotation angle of each of the loops goes below 360°.
 6. Themonopole antenna of claim 1, wherein the first bridge is disposed on arear surface of the dielectric substrate, and the second bridge isdisposed on the front surface of the dielectric substrate.
 7. Themonopole antenna of claim 6, wherein a Q-factor (Quality factor) and abandwidth are controllable by adjusting a rotation angle of theradiator.
 8. The monopole antenna of claim 7, wherein directivity iscontrollable by adjusting a rotation angle of each of the loops providedin the radiator.
 9. The monopole antenna of claim 8, wherein themonopole antenna has an omni-directional characteristic as the rotationangle of each of the loops approaches to 360°, and the directivity isincreased as the rotation angle of each of the loops goes below 360°.10. The monopole antenna of claim 1, wherein a Q-factor (Quality factor)and a bandwidth are controllable by adjusting a rotation angle of theradiator.
 11. The monopole antenna of claim 10, wherein directivity iscontrollable by adjusting a rotation angle of each of the loops providedin the radiator.
 12. The monopole antenna of claim 11, wherein themonopole antenna has an omni-directional characteristic as the rotationangle of each of the loops approaches to 360°, and the directivity isincreased as the rotation angle of each of the loops goes below 360°.13. The monopole antenna of claim 1, wherein a resonance frequency and areflection coefficient are adjustable by varying a thickness of each ofthe loops of the quasi-Moebius strip, a width of each of the first andsecond bridges, and a radius and a position of one or more of thevia-holes.